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An introduction to probabilistic methods with applications

Published online by Cambridge University Press:  26 August 2010

Pierre Del Moral  and
Nicolas G. Hadjiconstantinou
Pierre Del Moral
Affiliation:
Centre INRIA Bordeaux et Sud-Ouest & Institut de Mathématiques de Bordeaux, Université de Bordeaux I, 351 cours de la Libération, 33405 Talence Cedex, France. Pierre.Del-Moral@inria.fr
Nicolas G. Hadjiconstantinou
Affiliation:
Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge MA 02139-4307, USA. ngh@mit.edu
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Abstract

This special volume of the ESAIM Journal, Mathematical Modelling and Numerical Analysis,contains a collection of articles on probabilistic interpretations of some classes of nonlinear integro-differential equations.The selected contributions deal with a wide range of topics in applied probability theory and stochastic analysis, with applications in a variety of scientific disciplines, includingphysics, biology, fluid mechanics, molecular chemistry, financial mathematics and bayesian statistics. In this preface, we provide a brief presentation of the main contributions presented in this special volume. We have also included an introduction to classic probabilistic methods and a presentation of the more recent particle methods, with a synthetic picture of their mathematical foundations and their range of applications.

Keywords

Fokker-Planck equationsVlasov diffusion modelsfluid-Lagrangian-velocities modelBoltzmann collision modelsinteracting jump processesadaptive biasing force modelmolecular dynamicsground state energieshidden Markov chain problemsFeynman-Kac semigroupsDirichlet problems with boundary conditionsPoisson Boltzmann equationsmean field stochastic particle modelsstochastic analysisfunctional contraction inequalitiesuniformpropagation of chaos properties w.r.t. the time parameter

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